A large part of the problem IS that we, collectively, have forgotten how to board trains in an orderly fashion. As a friend would say, the passengers aren't stupid - just uninformed. Back in the heyday, people knew how to board trains, because boarding trains was something they did frequently - like crossing the street, or properly setting a table for a three-course meal. People knew and understood they had to get on the right train, to the right place - and to ASK if they were confused. Boarding a train is a collective skill, that if not used, will fade and disappear.
People today don't travel by train as much - so you get this mob mentality. Commuters may know that they need to follow the station signs to get on their train - but they have no concept of who's train it is. They see other trains, with different colors and logos, but they just assume they go to other places that they've never been. The average commuter knows hes at Providence, and going to Boston, and follows the signs accordingly. It never crosses his mind that he takes an MBTA train, and that there's a different AMTRAK train that also goes to the same place. To him, it's just the trains that arrive at the times the schedule in his pocket says. Any other trains don't matter to him. People don't associate the vehicle with their travel. (No one notices that its "a" #6 bus they take in the morning - but its not always the same physical bus, in the same colors, with the same signs. People don't notice that the PanAm airplane they got on says "TWA" on the side. They just know they need the #6 bus, or a PanAm flight. (Just using them as an example.)
The way we board airplanes, we REALLY treat people like cattle. You're checked, and checked again to make sure you're in the right place. There are zillions of signs directing you to your gate. Gates are generally known HOURS in advance. Everyone shows up early, then crams the waiting area until the plane boards. And people still cram on, or want to board early, to get luggage space before it fills up. (For some strange reason, we even let the premium-seat first class passengers board first, then get whacked by everyone elses luggage while they walk past them to get to their seats.) We treat people like cattle, so people get used to being hearded.
Then you drop these people in a train station - there's no separate terminals for different railroads. You have trains that make more then one stop (unlike most airplanes.) People are actually free to mill around - and they don't know what to do with themselves. There's no track assigned to the train - so people have no idea where to wait. Once a track is called, they all hurriedly run for the train, to make sure they're in the right place at the right time. They think maybe everyone else knows something they didn't, and the train might leave without them. Most of them probably assume that the poor person doing the ticket check won't let them on the wrong train. (It almost never happens at airports.)
They were on to something when they stuck a giant information booth right in the middle of Grand Central, where today we'd call it prime real estate for a Dunkin Donuts or Starbucks.
The way we're boarding the trains now gives passengers mixed signals. They see people, and assume they're there to help - even if they're just glorified gatekeepers. They don't have enough information to make informed judgements on their own, and learn to deal with the consequences of missing a train either. Either force people to go more on their own and learn, or make the human help actually. . .helpful. (Yes, I know how hard that could be.)
Let me provide a quick example of something that we know and do, but wouldn't be totally obvious to an outsider. We all know how to use an elevator - get in, push the button for your floor, get off at your floor. It's easy, right? Well imagine a 1920s passenger trying to use a modern elevator. They're used to elevators with human operators - you tell the guy where you want to go, and he does all the rest. We know that elevators do things automatically - like opening and closing the doors. Someone from the 1920's doesn't, They see a giant wall of numbered buttons, an open door button, a close door button, and a call button. So what do you do? Push the call button to call the operator? Push the door close button to close the door, then wonder why nothing happens? So once the elevator starts moving, you can't see the floor numbers in the elevator shaft - so how do you know where you are? More importantly, how do you tell the elevator to stop? The same way someone from the 1920's doesn't know how to use an elevator, we don't know how to board a train. Its not always a question of what to do - but how to do it.